Variational problems of potential theory

A series of variational problems are formulated and investigated on classes of charges, associated with space condensers. Solvability statements are established and the properties of the investigated extremal quantities are studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 347–354, March, 1991.     

Variational problems of potential theory

A series of variational problems are formulated and investigated on classes of charges, associated with space condensers. Solvability statements are established and the properties of the investigated extremal quantities are studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 347–354, March, 1991.     

A note on semi-open sets in fuzzy topological spaces

Concepts of semi-T_i (i = 0, 1, 2) spaces and semi-R_i (i = 0, 1) spaces are introduced and some fuzzy topological properties are investigated under the above mentioned axioms. Some mappings involving semi-open sets on fuzzy topological spaces are also introduced and investigated.     

Some a priori estimates of solutions to the Maxwell equations

In this paper, we present a collection of a priori estimates of the electromagnetic field scattered by a general bounded domain. The constitutive relations of the scatterer are in general anisotropic. Surface averages are investigated, and several results on the decay of these averages are presented. The norm of the exterior Calderón operator for a sphere is investigated and depicted as a function of the frequency. Copyright © 2014 John Wiley & Sons, Ltd.     

Stability of solutions of a system of linear differential equations with periodic stochastic coefficients

Systems of equations for first and second moments are investigated and transformed. Stability of solutions of a first-order linear differential equations is analyzed. Stability of solutions of the stochastic Mathieu equation is investigated and the boundaries of the instability region are determined.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 58, pp. 119–126, 1986.     

Compacton and generalized kink wave solutions of the CH-DP equation

The CH-DP equation is investigated by using the bifurcation method of planar systems and simulation method of differential equations. The bifurcation phase portraits are drawn in different regions of parameter plane. The planar graphs of compactons and generalized kink waves are simulated by using mathematical software Maple. Exact explicit parameter expressions of compactons and implicit expressions of generalized kink wave solutions are given, and the dynamic characters of these solutions are investigated.     

Investigation of the extremal directions in a glass-reinforced plastic

The extremal directions in an orthotropic material are investigated on the basis of six experimentally determined values of the investigated characteristic in the three planes of symmetry of the material.Translated from Mekhanika Polimerov, No. 4, pp. 742–745, July–August, 1971.     

Exact compacton and generalized kink wave solutions of the extended reduced Ostrovsky equation

The extended reduced Ostrovsky equation (EX-ROE) are investigated by using the bifurcation method of planar systems and simulation method of differential equations. The bifurcation phase portraits are drawn in different regions of parameter plane. The planar graphs of the compactons and the generalized kink waves are simulated by using software Maple. Exact explicit parameter expressions of the compactons and implicit expressions of the generalized kink wave solutions are given. The dynamic behavior of these solutions are also investigated.     

Normal families of functions and groups of pseudoconformal diffeomorphisms of quaternion and octonion variables

This paper is devoted to the specific class of pseudoconformal mappings of quaternion and octonion variables. Normal families of such functions are defined and investigated. Four criteria of a family to be normal are proved. Then groups of pseudoconformal diffeomorphisms of quaternion and octonion manifolds are investigated. It is proved that they are finite-dimensional Lie groups for compact manifolds. Their examples are given. Many characteristic features are found in comparison with commutatiive geometry over R or C. __________ Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 18, Functional Analysis, 2006.     

Local powers of two-sample and multi-sample rank tests for Lehmann's contaminated alternative

Summary Local powers of two- andk-sample rank tests under alternatives of contaminated distributions are investigated. It is shown that the rank tests based on normal scores and Wilcoxon scores are superior to thet-test or theF-test for many choices of alternatives of contaminated distributions and that the values of the asymptotic relative efficiency of the rank test based on Wilcoxon scores with respect to the normal scores are about one in all the investigated cases.     

A two-grid method for elliptic problem with boundary layers

A two-grid method for the elliptic equation with a small parameter ε multiplying the highest derivative is investigated. The difference schemes with the property of ε-uniform convergence on a uniform mesh and on Shishkin mesh are considered. In both cases, a two-grid method for resolving the difference scheme is investigated. A two-grid method has features that are concerned with a uniform convergence of a difference scheme. To increase the accuracy, the Richardson extrapolation in two-grid method is applied. Numerical results are discussed.     

Rings whose nilpotents form a multiplicative set

Nilpotents in Armendariz and abelian π-regular rings are multiplicatively closed. However, this fact need not hold in many kinds of rings. This article concerns a class of rings whose nilpotents are closed under multiplication. Rings contained in this class are said to be nilpotent-closed, and the structure of nilpotent-closed rings is investigated in relation with various situations which happen ordinarily in the study of noncommutative ring theory. In the procedure, various sorts of rings are investigated, so that they are nilpotent-closed. We also study familiar conditions under which nilpotents in nilpotent-closed rings form a subring.     

Fuzzy closure spaces

Fuzzy topological spaces do not constitute a natural boundary for the validity of theorems, but many results can be extended to what are called fuzzy closure spaces (or fcs's, for short). The notions of a subspace, a sum, and a product are extended to fcs's. The hereditary, additivity, and productivity behaviour of compactness in fcs's is investigated and some weak forms of compactness and fuzzy continuous functions in fcs's are introduced. The interaction between fuzzy proximity spaces and fcs's is investigated; A necessary background is included for completeness.     

Banach algebras with unique uniform norm

Commutative semisimple Banach algebras that admit exactly one uniform norm (not necessarily complete) are investigated. This unique uniform norm property is completely characterized in terms of each of spectral radius, Silov boundary, set of uniqueness, semisimple norms; and its connection with recently investigated concepts like spectral extension property, multiplicative Hahn Banach extension property and permanent radius are revealed. Several classes of Banach algebras having this property as well as those not having this property are discussed.

     

Properties of discrete Chebyshev collocation differential operators in curvilinear geometries

The properties of discrete systems resulting from spectral Chebyshev collocation discretizations are investigated with respect to the solution efficiency of corresponding solvers. Complex geometries are encountered by a mapping technique to connect computational and physical domains. Several representative transformation techniques are considered. The influences of the differential operators, the boundary conditions, the geometry, and the number of grid points are systematically studied. The convergence properties of the BiCGSTAB method when iteratively solving the discrete systems are investigated. Copyright © 2008 John Wiley & Sons, Ltd.     

Numerical Analysis of the Synchronization of Coupled Chemical Oscillators

A reaction–diffusion model describing a system of coupled oscillators is constructed and investigated. The oscillators in this study are chemical oscillators that represent an oscillatory heterogeneous catalytic reaction in a granular catalyst layer. The oscillators are arranged serially in the reagent stream and are coupled through the gaseous phase. The dynamic behavior of the system is investigated as a function of the main external parameter — the partial pressure of one of the reagents in the gaseous phase. Existence regions of regular and chaotic oscillations are identified. Synchronization conditions are established for the oscillations in such a chain of coupled chemical oscillators.     

Quasi-Invariant and Pseudo-Differentiable Measures with Values in Non-Archimedean Fields on a Non-Archimedean Banach Space

Quasi-invariant and pseudo-differentiable measures on a Banach space X over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in non-Archimedean fields, for example, the field Q _p of p-adic numbers. Theorems and criteria are formulated and proved about quasi-invariance and pseudo-differentiability of measures relative to linear and non-linear operators on X. Characteristic functionals of measures are studied. Moreover, the non-Archimedean analogs of the Bochner-Kolmogorov and Minlos-Sazonov theorems are investigated. Infinite products of measures are considered and the analog of the Kakutani theorem is proved. Convergence of quasi-invariant and pseudo-differentiable measures in the corresponding spaces of measures is investigated.__________Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 1, pp. 149–199, 2003.     

The expected discounted penalty function under a risk model with stochastic income

Quantities of interest in ruin theory are investigated under the general framework of the expected discounted penalty function, assuming a risk model where both premiums and claims follow compound Poisson processes. Both a defective renewal equation and an integral equation satisfied by the expected discounted penalty function are established. Some implications that these equations have on particular quantities such as the discounted deficit and the probability of ultimate ruin are illustrated. Finally, the case when premiums have Erlang(n,β) distribution and the distribution of the claims is arbitrary is investigated in more depth. Throughout the paper specific examples where claims and premiums have particular distributions are provided.     

Reliability Studies of Bivariate Distributions with Pareto Conditionals

In this paper we study Arnold's (1987, Statist. Probab. Lett.5, 263–266) class of bivariate distributions with Pareto conditionals from a reliability point of view. Failure rates and mean residual life function of the marginal distributions and their monotonic properties are studied. The hazard components and their properties are investigated and their relationships with some measures of dependence are established. Finally, the failure rate of the minimum of the two components is examined and its monotonicity is investigated. Some of the results presented here are general and would be useful in studying the dependence structure in other classes of bivariate distributions.     

Splineapproximationen von beliebigem Defekt zur numerischen Lösung gewöhnlicher Differentialgleichungen. Teil I

Summary In 1967, F.R. Loscalzo und T.D. Talbot presented a procedure for obtaining polynomial spline approximations of defect one for solutions of the initial value problem for first order ordinary differential equations. This method is generalized and investigated for spline approximations of arbitrary defect. The results are analogous to those of the defect one. In the first part of this paper the divergence problem is treated. The convergent procedures are investigated in a following second part of this paper.